# The Shape Dependence of Vainshtein Screening in the Cosmic Matter Bispectrum

## TL;DR

This paper investigates how the shape-dependent Vainshtein screening affects the cosmic matter bispectrum in modified gravity theories, providing analytic expressions and quantifying the effect's scale and magnitude.

## Contribution

It derives the shape dependence signature of Vainshtein screening on the matter bispectrum using a second order perturbative analysis in a cubic Galileon model.

## Key findings

- Shape dependence enters the bispectrum with a scale-factor dependence of a^{3/2}.
- The effect magnitude today can reach up to 2%.
- Deviations from ΛCDM linear growth rate can be up to 5%.

## Abstract

One of the most pressing questions in modified gravity is how deviations from general relativity can manifest in upcoming galaxy surveys. This is especially relevant for theories exhibiting Vainshtein screening, where such deviations are efficiently suppressed within a (typically large) Vainshtein radius. However, Vainshtein screening is known to be shape dependent: it is most effective around spherical sources, weaker around cylindrical objects and completely absent for planar sources. The Cosmic Web therefore offers a testing ground, as it displays many shapes in the form of clusters, filaments and walls. In this work, we explicitly derive the signature of the shape dependence of Vainshtein screening on the matter bispectrum, by considering a cubic Galileon model with a conformal coupling to matter and a cosmological constant. We perform a second order perturbative analysis, deriving analytic, integral expressions for the bispectrum, which we integrate using hi_class. We find that the shape dependence of Vainshtein screening enters the bispectrum with a unique scale-factor dependence of $\propto a^{3/2}$. The magnitude of the effect today is up to 2 % for a model whose linear growth rate deviates up to 5 % from $\Lambda$CDM.